\(O\) -Notation. The use of the \(O\) -notation is somewhat subtle
when multiple inputs/variables and exponential functions are involved.
Regarding the multiple inputs, we follow the standard convention that
is mentioned in [1]} and actually rather well explained on the
Wikipedia page on “Big \(O\)  Notation”. Assume that we have three
variables \(n,m,k\) . When writing something like
\(f(n,m,k) \in n \cdot 2^{m \cdot 2^{O(k)}}\)  what we mean is
\(\log \log f(n,m,k) \in O(\log \log n \cdot \log m \cdot k).\) 
